x 1 2 3 4 5 y 1 4 9 16 25 Look at the table and choose “true” or “false”.

Question

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(5 points)
TrueFalseThis table represents a function.
This table shows an increasing relationship.
This table shows a linear relationship.
This table shows a constant rate of change.
This table shows a proportional relationship.
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Answer 1

Let's analyze each statement based on the data provided in the table where the values of \(x\) are 1, 2, 3, 4, 5 and the corresponding values of \(y\) are 1, 4, 9, 16, 25.

1. This table represents a function.
   True - Each \(x\) value corresponds to exactly one \(y\) value.

2. This table shows an increasing relationship.
   True - As \(x\) increases, \(y\) also increases.

3. This table shows a linear relationship.
   False - The relationship is not linear because the differences between the \(y\) values are not constant. For example, the difference between 1 and 4 is 3, between 4 and 9 is 5, and so on.

4. This table shows a constant rate of change.
   False - The rate of change is not constant as evidenced by the changing differences mentioned earlier.

5. This table shows a proportional relationship.
   False - A proportional relationship would mean that \(y\) is directly proportional to \(x\) (i.e., \(y = kx\) for some constant \(k\)), which is not the case here.

Overall, the answers are:

1. True
2. True
3. False
4. False
5. False